Question

If f(x)=3x+2 and g(x)=√2x+5, then find (fog) (1)​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{fog(1)=3\sqrt{2}+17}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies f(x) = 3x + 2\\ \\ \tt: \implies g(x) = \sqrt{2}{x}+5 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies fog(1)=?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies fog(x) = f(g(x)) \\ \\ \tt: \implies fog(x) = f( \sqrt{2}x + 5) \\ \\ \tt: \implies fog(x) = 3(\sqrt{2}x + 5) + 2 \\ \\ \tt: \implies fog(x)= 3\sqrt{2}x+15+2 \\ \\ \green{\tt: \implies fog(x) = 3\sqrt{2}x+17}$

$\tt: \implies fog(1) = 3\sqrt{2} \times 1 + 17 \\ \\ \green{\tt: \implies fog(1) = 3 \sqrt{2} + 17} \\ \\ \green{\tt \therefore \tt: \implies fog(1) \: is \: 3 \sqrt{2} + 17}$

Answer 2

$\green{ \underline \bold{fog(1) = 3 \sqrt{2} + 17 : }} \\ \orange{ \underline \bold{given: }} \\ \tt : \implies \: f(x) = 3x + 2 \\ \tt : \implies \: g(x) = \sqrt{2x + 5} \\ \\ \blue{ \underline \bold{to \: find: }} \\ \tt : \implies \: fog(1) = ? \\ \green{ \underline \bold{as \: we \: know : }} \\ \tt : \implies \: fog(x) = f(g(x)) \\ \tt : \implies \: fog(x) = f( \sqrt{2} x + 5) \\ \tt : \implies \: fog(x) = 3( \sqrt{2} + 5x) + 2 \\ \tt : \implies \: fog(x) = 3 \sqrt{2} + 15 + 2 \\ \\ \\ \green{ \underline \bold{se \: now : }}\tt : \implies \: fog (x) = 3 \sqrt{2} \times 1 + 17 \\ \tt : \implies \: fog(1) = 3\sqrt{2 \times 1 + 17} \\ \\ \\ \pink{ \underline \bold{ \tt : \implies: fog(1) = 3 \sqrt{2} + 17 }} \\ \\ \red{ \underline \bold{\tt : \implies \: fog(1)is \: 3 \sqrt{2 + 17} : }}$